Nonlinear Vibrations of an Unbalance Rotor with Radial Clearance

Madeleine Pascal

Laboratoire Systèmes Complexes, Université d’Evry

Val d’Essonne, 40 rue du Pelvoux, 91025, EVRY cedex; France

e-mail:    mpascal@iup.univ-evry.fr

 

The work originates from phenomena observed in large commercial jet aircraft when fan blade off occurs. The unbalance produced by this event induces the bending of the shafts of the motor engine, and during this motion, several contacts may appear. After a transient phase, the main rotor of the aircraft engine reaches a so called “windmilling motion” inside some frequencies range depending on the velocity and on the altitude of the aircraft. Jump and hysteretic phenomena are observed during this motion. In the past, several dynamical models were used for the prediction of rotor dynamical behavior. The first model taking into account the contact between the rotor and the casing is the Jeffcott rotor. The nonlinear behavior induced by this contact was first investigated in different works: a physical model with two degrees of freedom, which represents the rotor system with a bearing clearance; several other investigators use more complex models including friction effect, onset condition for the dry whip, cross-coupling stiffness forces, …

In this work, the simplified model is used with the addition of a snubbing stiffness in order to take into account the deformations occurring near the contact zone. Analytical solutions for the whirling motions of the rotor are obtained; a non dimensional analysis is performed in order to explain the mechanism leading to jump phenomenon and a detailed study of the stability conditions for these motions is performed.

An attempt to understand the non linear behavior observed in an aircraft engine, when fan blade off occurs, has been performed  using a simplified model for which analytical solutions can be found. Several parameters of fundamental importance on the characteristics of the system behavior have been identified. The paper deals with the non linear vibrations of a rotating machinery in presence of unbalance and eventual contact with the casing. After a transient phase, the rotor reaches a so called “windmilling” motion inside some frequencies range. Jump and hysteretic phenomena are observed during this motion. A simplified model with two degrees of freedom which represents the rotor system with a bearing clearance is used in order to obtain analytical solutions leading to jump phenomenon. Stability conditions of these whirling motions are discussed.